Exercise 4

Return your answers by noon of Wed, Oct 14.

1. Find a Pade approximation of the form (a+bx+cx**2)/(1+dx+ex**2) for the sine functiion.

2. Make a module containing the declaration of a data type vector for handling vectors, and functions for evaluating scalar, vector, scalar triple and vector triple products of vectors. Test the module with a main program.

3. Define also a type polar that contains the spherical coordinates corresponding to a vector. Define the assignment operator so that the conversions between rectangular and spherical coordinates can be accomplished as

   type (vector) :: v, w
   type (polar) :: p
   ...
   p = v
   w = p

4. Create a table containing the sines of 0, 10, ... 350 degrees. Write a function for interpolating sines of intermediate values. Take care that the function works correctly also for angles over 350 degrees (i.e. when the angle goes from 350 to 0).